En poursuivant votre navigation sur ce site, vous acceptez l'utilisation d'un simple cookie d'identification. Aucune autre exploitation n'est faite de ce cookie. OK

Bibliothèque Mathematique Audiovisuelle

Bibliothèque Mathematique Audiovisuelle

1

Diffusion asymptotic of a kinetic model for gas-particle mixture with energy exchanges

Sélection

Cochez un dossier pour ajouter l'enregistrement à vos favoris. Décochez-le pour l'en enlever.

4

gerer mes paniers

Signaler une erreur
Multi angle
Auteurs : Charles, Frédérique (Auteur de la conférence)
CIRM (Editeur )

Loading the player...
Résumé : In this talk we present a non-isothermal kinetic model of the interactions between dust particles and gas molecules. We assume that gas-dust collisions follow a diffuse reflection mechanism at the surface of the dust particles as in [1] and [2]. The surface temperature of the particles is treated as a function of time and space, satisfying a transport-like equation. The highlight of this model is that it allows to derive both the conservation of the total energy of the system and an explicit expression of the entropy. After dimensionalizing the equations, we carry out a formal diffusive asymptotics for a two-species Maxwell-Stefan model, with several small model parameters tending towards zero. This is a joint work with Annamaria Massimini and Francesco Salvarani [3].

Mots-Clés : kinetic theory; Boltzmann equation; diffusive asymptotics

Codes MSC :
76P05 - Rarefied gas flows, Boltzmann equation, See also {82B40, 82C40, 82D05}
 74A25 - Molecular, statistical, and kinetic theories
    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de Publication : 04/04/2025
    Date de Captation : 27/03/2025
    Sous Collection : Research talks
    Catégorie arXiv : Analysis of PDEs
    Domaine(s) : EDP
    Format : MP4 (.mp4) - HD
    Durée : 00:44:30
    Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2025-03-27_Charles.mp4
Informations sur la Rencontre

Nom de la Rencontre : SMF RC. Kinetic theory and fluid mechanics: couplings, scalings and asymptotics. / ER SMF. Théorie cinétique et mécanique des fluides : couplages, échelles et asymptotiques.
Organisateurs de la Rencontre : Han-Kwan, Daniel ; Lods, Bertrand ; Moussa, Ayman ; Tristani, Isabelle
Dates : 24/03/2025 - 28/03/2025
Année de la rencontre : 2025
URL de la Rencontre : https://conferences.cirm-math.fr/3205.html

Données de citation

DOI : 10.24350/CIRM.V.20331503
Citer cette vidéo: Charles, Frédérique (2025). Diffusion asymptotic of a kinetic model for gas-particle mixture with energy exchanges. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20331503
URI : http://dx.doi.org/10.24350/CIRM.V.20331503

Voir Aussi

Bibliographie

  • ANWASIA, Benjamin, BISI, Marzia, SALVARANI, Francesco, et al. On the Maxwell-Stefan diffusion limit for a reactive mixture of polyatomic gases in non-isothermal setting. Kinetic and Related Models, 2020, 13(1): 63-95. - https://doi.org/10.3934/krm.2020003

  • ANWASIA, Benjamin, GONÇALVES, Patrícia, et SOARES, Ana Jacinta. On the formal derivation of the reactive Maxwell-Stefan equations from the kinetic theory. Europhysics Letters, 2020, vol. 129, no 4, p. 40005. - https://doi.org/10.1209/0295-5075/129/40005

  • ANWASIA, Benjamin, GONÇALVES, Patrícia, et SOARES, Ana Jacinta. From the simple reacting sphere kinetic model to the reaction-diffusion system of Maxwell-Stefan type.Communications in Mathematical Sciences, 2019, vol. 17, no 2, p. 507-538 - https://dx.doi.org/10.4310/CMS.2019.v17.n2.a9

  • BONDESAN, Andrea et BRIANT, Marc. Stability of the Maxwell–Stefan system in the diffusion asymptotics of the Boltzmann multi-species equation. Communications in Mathematical Physics, 2021, vol. 382, no 1, p. 381-440. - https://doi.org/10.1007/s00220-021-03976-5

  • BOTHE, Dieter. On the Maxwell-Stefan approach to multicomponent diffusion. In : Parabolic problems: the Herbert Amann festschrift. Basel : Springer Basel, 2011. p. 81-93. - https://doi.org/10.1007/978-3-0348-0075-4_5

  • BOUDIN, Laurent, GREC, Bérénice, et PAVAN, Vincent. The Maxwell–Stefan diffusion limit for a kinetic model of mixtures with general cross sections. Nonlinear Analysis, 2017, vol. 159, p. 40-61. - https://doi.org/10.1016/j.na.2017.01.010

  • BOUDIN, Laurent, GREC, Bérénice, et SALVARANI, Francesco. A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations. Discrete and Continuous Dynamical Systems-Series B, 2012, vol. 17, no 5, p. 1427-1440. - https://doi.org/10.3934/dcdsb.2012.17.1427

  • BOUDIN, Laurent, GREC, Bérénice, et SALVARANI, Francesco. The Maxwell-Stefan diffusion limit for a kinetic model of mixtures. Acta Applicandae Mathematicae, 2015, vol. 136, p. 79-90. - https://doi.org/10.1007/s10440-014-9886-z

  • CERCIGNANI, Carlo. The boltzmann equation. Springer New York, 1988. - https://doi.org/10.1007/978-1-4612-1039-9_2

  • CERCIGNANI, Carlo. Rarefied gas dynamics: from basic concepts to actual calculations. Cambridge university press, 2000. -

  • CHARLES, Frédérique. Kinetic modelling and numerical simulations using particle methods for the transport of dust in a rarefied gas. In : 26th International Symposium on Rarified Gas Dynamics (RGD26). American Institute of Physics, 2008. p. 409-414. - https://doi.org/10.1063/1.3076512

  • CHARLES, Frédérique. Modélisation mathématique et étude numérique d'un aérosol dans un gaz raréfié. Application à la simulation du transport de particules de poussière en cas d'accident de perte de vide dans ITER. 2009. Thèse de doctorat. École normale supérieure de Cachan-ENS Cachan. - https://theses.hal.science/tel-00463639/

  • Frédérique Charles. Développement de modèles et analyse de méthodes numériques pour des problèmes cinétiques issus de la physique des plasmas et des écoulements gaz-particules. Sorbonne Université, 2021. - https://hal.science/tel-04119380/document

  • CHARLES, Frédérique, DELLACHERIE, Stéphane, et SEGRÉ, Jacques. Kinetic modeling of the transport of dust particles in a rarefied atmosphere. Mathematical Models and Methods in Applied Sciences, 2012, vol. 22, no 04, p. 1150021. - https://doi.org/10.1142/S0218202511500217

  • CHARLES, Frédérique et DESVILLETTES, Laurent. From collisional kinetic models to sprays: internal energy exchanges. Communications in Mathematical Sciences, 2025, vol. 23, no 1, p. 173--193. - https://dx.doi.org/10.4310/CMS.241217081314

  • CUNNINGHAM, Ebenezer. On the velocity of steady fall of spherical particles through fluid medium. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1910, vol. 83, no 563, p. 357-365. - https://doi.org/10.1098/rspa.1910.0024

  • DEGOND, Pierre et LUCQUIN-DESREUX, Brigitte. The asymptotics of collision operators for two species of particles of disparate masses. Mathematical Models and Methods in Applied Sciences, 1996, vol. 6, no 03, p. 405-436. - https://doi.org/10.1142/S0218202596000158

  • DESVILLETTES, Laurent, GOLSE, François, et RICCI, Valeria. A formal passage from a system of boltzmann equations for mixtures towards a Vlasov-Euler system of compressible fluids. Acta Mathematicae Applicatae Sinica, English Series, 2019, vol. 35, p. 158-173. - https://doi.org/10.1007/s10255-019-0802-1

  • ERN, Alexandre et GIOVANGIGLI, Vincent. Multicomponent transport algorithms. Springer Science & Business Media, 1994. - https://doi.org/10.1007/978-3-540-48650-3

  • FICK, Adolph. V. On liquid diffusion. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1855, vol. 10, no 63, p. 30-39. - https://doi.org/10.1080/14786445508641925

  • FICK, Adolph. Ueber Diffusion. Poggendorff's Annel Physik, 94:59--86, 1855. - https://doi.org/10.1002/andp.18551700105

  • GIOVANGIGLI, Vincent.Multicomponent flow modeling. Modeling and Simulation in Science, Engineering and Technology. Birk Boston, Inc., Boston, MA, 1999. -

  • HUTRIDURGA, Harsha et SALVARANI, Francesco. On the Maxwell–Stefan diffusion limit for a mixture of monatomic gases. Mathematical Methods in the Applied Sciences, 2017, vol. 40, no 3, p. 803-813. - https://doi.org/10.1002/mma.4013

  • HUTRIDURGA, Harsha et SALVARANI, Francesco. On the Maxwell–Stefan diffusion limit for a mixture of monatomic gases. Mathematical Methods in the Applied Sciences, 2017, vol. 40, no 3, p. 803-813. - https://doi.org/10.1002/mma.4013

  • CLERK MAXWELL, J. On the dynamical theory of gases. Philosophical Transactions of the Royal Society of London Series I, 1867, vol. 157, p. 49-88. - https://doi.org/10.1098/rstl.1867.0004

  • OTTERMAN, Bernard et LEVINE, Andrew S. Analysis of gas-solid particle flows in shock tubes. AIAA Journal, 1974, vol. 12, no 5, p. 579-580. - https://doi.org/10.2514/3.49300

  • STEFAN, Josef. Über das Gleichgewicht und die Bewegung, insbesondere die Diffusion von Gasgemengen. Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Classe der Kaiserlichen Akademie der Wissenschaften Wien, 2te Abteilung, 1871, vol. 63, p. 63-124. - https://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/18237

  • TAYLOR, R., et KRISHNA R. . Multicomponent Mass Transfer, John Wiley, New York, USA,1992. 580 p. - https://doi.org/10.1002/apj.5500020408

  • VIGNOLES, Gérard L., CHARRIER, Pierre, PREUX, Christophe, et al. Rarefied pure gas transport in non-isothermal porous media: effective transport properties from homogenization of the kinetic equation. Transport in Porous Media, 2008, vol. 73, no 2, p. 211-232. - https://doi.org/10.1007/s11242-007-9167-7

  • VILLANI, Cédric, Chap. 2 - A Review of Mathematical Topics in Collisional Kinetic Theory, S. Friedlander, D. Serre, Handbook of Mathematical Fluid Dynamics,
    North-Holland, Vol. 1, 2002, Pages 71-74 - https://doi.org/10.1016/S1874-5792(02)80004-0

  • VILLANI, Cédric, Mathematics of Granular Materials. J Stat Phys 124, 2006 p. 781–822 - https://doi.org/10.1007/s10955-006-9038-6


Imagette Video

Sélection

Cochez un dossier pour ajouter l'enregistrement à vos favoris. Décochez-le pour l'en enlever.

4

gerer mes paniers

Signaler une erreur